Downside risk in multiperiod tracking error models

The recent crisis made it evident that replicating the performance of a benchmark is not a sufficient goal to meet the expectations of usually risk-averse investors. The manager should also consider that the investors are seeking downside protection when the benchmark performs poorly and thus they should integrate a form of downside risk control. We propose a multiperiod double tracking error portfolio model which combines these two goals and provides enough flexibility. In particular, the control of the downside risk is carried out through the presence of a floor benchmark with respect to which we can accept different levels of shortfall. The choice of a proper measure for downside risk leads to different problem formulations and investment strategies which can reflect different attitudes towards risk. The proposed model is tested through a set of out-of-sample rolling simulations in different market conditions.